Such a clutch outer member for a multi-plate clutch is already known, as disclosed in Patent Publication 1 below, in which the annular connecting part suppresses radially outward deformation of each fin due to centrifugal force during high-speed rotation of the clutch and always maintains an appropriate sliding fit between the spline grooves and spline teeth on the outer periphery of a friction plate, thus contributing to operational stability and durability of the clutch.    Patent Publication 1: Japanese Patent Application Laid-open No. 2005-257032